Barracuda won't roll

Easy. The rear axle was never designed to work like that. The pinion has no support with the nut and pinion off, and is "falling into" the pinion, becoming a nice solid doorstop

The reason one wheel turns opposite is that you have an "open" or "single track" that is "non" limited slip or "non" suregrip axle.

Because the ring is locked, one axle is turning the other through the spider gears